In this paper we study the implementation of a variant of the classic Gauss-Jordan (GJ) method which was recently introduced by Huard [8] on a shared memoryMIMDcomputer. Two parallel versions are derived by dividing the sequential Huard method into noninterfering tasks. Taking into consideration the computation as well as the communication complexity we present a parallel scheduling algorithm for each task graph. Next, in an attempt to reduce the communication cost we introduce block versions and follow a similar approach for their study.